Effect of Gas Flow Rate and Gas Composition in Ar/CH4 Inductively Coupled Plasmas
1
October 14, 2011
Keisoku Engineering System Co., Ltd., JAPAN
Dr. Lizhu Tong
COMSOL CONFERENCE BOSTON 2011
2
Contents
1. Plasma processing and nonequilibrium discharge
2. Plasma simulation using COMSOL Multiphysics
3. Ar/CH4 ICP plasma model
4. Results
5. Conclusions
Plasma processing and nonequilibrium discharge (1)
3
Plasma processing has been used for fabricating semiconductors. In order to make a hyperfine feature on the wafer, a high aspect-ratio etching is needed.
Low gas pressure in etching
The energy of ions incident on the wafer must be controlled to realize an accurate and reliable processing.
Nonequilibrium discharge
4
For low pressure discharges the plasma is not in thermal equilibrium.
In the bulk plasma, the electron temperature Te greatly exceeds the ion
temperature Ti and neutral gas temperature Tg.
Low
temperature
plasma
Plasma processing and nonequilibrium discharge (2)
Pressure
Thermal plasma
Types of plasma involved in COMSOL Multiphysics
5
The common types of plasma: • Inductively coupled plasma (ICP) • DC discharge • Microwave plasma • Electrical breakdown • Capacitively coupled plasma (CCP) • Combined ICP/CCP reactor
6
Plasma module physics interfaces
• The drift diffusion interface • The heavy species transport interface • The Boltzmann equation, Two-term approximation interface • The inductively coupled plasma interface (ICP) • The microwave plasma interface • The capacitively coupled plasma interface (CCP) • The DC discharge interface
Plasma module format in COMSOL Multiphysics
7
Plasma interfaces Plasma model library
Neutrals (7)
CH4
C2H2,C2H4,C2H6,C3H8
H2,Ar
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Electron reactions included in the model
Plasma chemistry (1) No. Reaction
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
Ions (13)
Radicals (5)
CH,CH2,CH3,CH5
H
Excited species (5)
CH4*(2vib.), H(2p,3p), Ar*
9
Plasma chemistry (2)
Reactions of ion and neutral species
No. Reaction
34 35 36 37 38 39 40 41
Reactions among neutral species
No. Reaction
42 43 44 45 46 47 48 49 50 51 52 53 54 55 56
10
COMSOL Multiphysics solves a pair of drift diffusion equation for the electron density and electron energy density.
Electron transport
Source term Source term
Rate coefficient
Electron transport boundary conditions
11
There are a variety of boundary conditions available for the electrons: Wall which includes the effects of : Secondary electron emission Thermionic emission Electron reflection Flux which allows you to specify an arbitrary influx for the electron density and electron energy density. Fixed electron density and mean electron energy Insulation
12
Heavy species transport
Transport of the heavy species (non-electron species) is determined from solving a modified form of the Maxwell-Stefan equations :
The multiphysics interfaces contain an integrated reaction manager to keep track of the electron impact reactions, reactions, surface reactions and species.
where
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Gas flow transport
The neutral gas flow is determined by the Navier-stokes equations :
Conservation of momentum
Conservation of mass
where
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Electrostatic field
Electromagnetic field
For inductive discharges we solve the magnetic field in the frequency domain:
The plasma potential is computed from Poisson’s equation:
The space charge is computed from the number densities of electrons and other charged species.
15
Ar/CH4 ICP plasma model (1)
ICP plasma model Computational conditions
Gas： Ar/CH4 mixtures RF frequency：13.56 MHz Operating pressure：20 mTorr Temperature：300 K Input power: 300 W Fluid flow：laminar Gas flow rate：20-1000 sccm Ar fractions: 0-1 EEDF (Electron energy distribution function): Druyvesteynian
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Coupled simulation of plasma and fluid flow
Plasma
Ar/CH4 ICP plasma model (2)
Fluid flow
Flow velocity u and pressure p
Density and Dynamic viscosity
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Results (1) Discharge structure in a 95%Ar/5%CH4 ICP plasma at a gas flow of 50 sccm
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Results (2)
Ar+ C2H5+
CH5+
CH4+ CH3
+
Electron and ion densities
19
Results (3)
CH
CH2 CH3
H atom
Radical number density
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Results (4)
1E+15
1E+16
1E+17
1E+18
1E+19
0 200 400 600 800 1000
Ele
ctro
n de
nsity
(m-3
)
Flow rate (sccm)
0%Ar50%Ar95%Ar100%Ar
0
1
2
3
4
5
6
0 200 400 600 800 1000
Ele
ctro
n te
mpe
ratu
re (e
V)
Flow rate (sccm)
0%Ar50%Ar95%Ar100%Ar 1E+15
1E+16
1E+17
1E+18
1E+19
0 0.25 0.5 0.75 1
Ele
ctro
n de
nsity
(m-3
)
Ar fractions
20sccm100sccm500sccm1000sccm
Electron density (Gas flow rate: 20-1000 sccm)
Electron temperature (Gas flow rate: 20-1000 sccm)
Electron density (Ar fractions: 0 -1)
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Results (5)
1E+14
1E+15
1E+16
1E+17
1E+18
1E+19
1E+20
0 200 400 600 800 1000
Den
sity
(m-3
)
Flow rate (sccm)
50%Ar95%Ar100%Ar
Ar+
1E+14
1E+15
1E+16
1E+17
1E+18
1E+19
1E+20
0 200 400 600 800 1000
Den
sity
(m-3
)
Flow rate (sccm)
0%Ar50%Ar95%Ar
CH5+
1E+14
1E+15
1E+16
1E+17
1E+18
1E+19
1E+20
0 200 400 600 800 1000
Den
sity
(m-3
)
Flow rate (sccm)
0%Ar50%Ar95%Ar
C2H5+
1E+14
1E+15
1E+16
1E+17
1E+18
1E+19
1E+20
0 200 400 600 800 1000
Den
sity
(m-3
)
Flow rate (sccm)
0%Ar50%Ar95%Ar
CH4+
1E+14
1E+15
1E+16
1E+17
1E+18
1E+19
1E+20
0 200 400 600 800 1000
Den
sity
(m-3
)
Flow rate (sccm)
0%Ar50%Ar95%Ar
CH3+
Ion number density
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Results (6)
1E+14
1E+15
1E+16
1E+17
1E+18
1E+19
1E+20
0 200 400 600 800 1000
Den
sity
(m-3
)
Flow rate (sccm)
0%Ar50%Ar95%Ar
H atom
1E+14
1E+15
1E+16
1E+17
1E+18
1E+19
1E+20
0 200 400 600 800 1000
Den
sity
(m-3
)
Flow rate (sccm)
0%Ar50%Ar95%Ar
CH radical
1E+14
1E+15
1E+16
1E+17
1E+18
1E+19
1E+20
0 200 400 600 800 1000
Den
sity
(m-3
)
Flow rate (sccm)
0%Ar50%Ar95%Ar
CH2 radical
1E+14
1E+15
1E+16
1E+17
1E+18
1E+19
1E+20
0 200 400 600 800 1000
Den
sity
(m-3
)
Flow rate (sccm)
0%Ar50%Ar95%Ar
CH3 radical
Radical number density
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Conclusions
The simulations of low-pressure inductively coupled rf plasmas in Ar/CH4 were performed by coupling plasma simulation with fluid dynamics calculation.
It is found that the electron densities increased and electron temperatures decreased with a rise in gas flow rate for the different Ar fractions. The radicals CH3, CH2, CH, and H appeared the high densities over all the gas flow rates and different Ar fractions.
The gas flows presented the largest influence on plasma properties at a small amount (5%mol) of CH4 added to Ar.
⦁ From 20 to 1000 sccm, the densities of CH3+ ions increased one order
and those of CH5+ and C2H5
+ increased over two orders. The control of gas flow rate and gas composition would be very beneficial in
obtaining the deposition of good quality thin films. It could be concluded that by using COMSOL Multiphysics, the simulations in
actual plasma reactors could be realized by coupling with the calculations of CFD, heat transfer, electromagnetic field and etc..
Thank you for your attention
